Precalculus Essentials

Ratti and McWaters wrote this series with the primary goal of preparing students to be successful in calculus. Having taught both calculus and precalculus, the authors saw firsthand where students would struggle, where they needed help making connections, and what material they needed in order to succeed in calculus. Their experience in the classroom shows in each chapter, where they emphasize conceptual development, real-life applications, and extensive exercises to encourage a deeper understanding.

 

With a new addition to the series, Precalculus Essentials, this text offers the best of both worlds: fast-paced, rigorous topics and a friendly, “teacherly” tone. This text is developed with a focus on key topics for calculus preparation.

 

P. Basic Concepts of Algebra

P.1 The Real Numbers; Integer Exponents

P.2 Radicals and Rational Exponents

P.3 Solving Equations

P.4 Inequalities

P.5 Complex Numbers

 

1. Graphs and Functions

1.1 Graphs of Equations

1.2 Lines

1.3 Functions

1.4 A Library of Functions

1.5 Transformations of Functions

1.6 Combining Functions; Composite Functions

1.7 Inverse Functions

            Chapter 1 Summary

            Chapter 1 Review Exercises

            Chapter 1 Exercises for Calculus

            Chapter 1 Practice Test A

            Chapter 1 Practice Test B

 

2. Polynomial and Rational Functions

2.1 Quadratic Functions

2.2 Polynomial Functions

2.3 Dividing Polynomials and the Rational Zeros Test

2.4 Zeros of a Polynomial Function

2.5 Rational Functions

            Chapter 2 Summary

            Chapter 2 Review Exercises

            Chapter 2 Exercises for Calculus

            Chapter 2 Practice Test A

            Chapter 2 Practice Test B

 

3. Exponential and Logarithmic Functions

3.1 Exponential Functions

3.2 Logarithmic Functions

3.3 Rules of Logarithms

3.4 Exponential and Logarithmic Equations and Inequalities

            Chapter 3 Summary

            Chapter 3 Review Exercises

            Chapter 3 Exercises for Calculus

            Chapter 3 Practice Test A

            Chapter 3 Practice Test B

 

4. Trigonometric Functions

4.1 Angles and Their Measure

4.2 The Unit Circle; Trigonometric Functions

4.3 Graphs of the Sine and Cosine Functions

4.4 Graphs of the Other Trigonometric Functions

4.5 Inverse Trigonometric Functions

4.6 Right-Triangle Trigonometry

4.7 Trigonometric Identities

4.8 Sum and Difference Formulas

            Chapter 4 Summary

            Chapter 4 Review Exercises

            Chapter 4 Exercises for Calculus

            Chapter 4 Practice Test A

            Chapter 4 Practice Test B

 

5. Applications of Trigonometric Functions

5.1 The Law of Sines and the Law of Cosines

5.2 Areas of Polygons Using Trigonometry

5.3 Polar Coordinates

5.4 Parametric Equations

            Chapter 5 Summary

            Chapter 5 Review Exercises

            Chapter 5 Exercises for Calculus

            Chapter 5 Practice Test A

            Chapter 5 Practice Test B

 

6. Further Topics in Algebra

6.1 Sequences and Series

6.2 Arithmetic Sequences; Partial Sums

6.3 Geometric Sequences and Series

6.4 Systems of Equations in Two Variables

6.5 Partial-Fraction Decomposition

            Chapter 6 Summary

            Chapter 6 Review Exercises

            Chapter 6 Exercises for Calculus

            Chapter 6 Practice Test A

            Chapter 6 Practice Test B

 

Appendix: Answers to Practice Problems